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ISEE Upper Level Math : Exponents

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Example Questions

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Example Question #1 :How To Multiply Exponents

If x=2 , find the value of:

$\frac{3x^{\sqrt{2}}(x^{\sqrt{3}})^\sqrt{3}}{x^{\sqrt{2}}}$

Possible Answers:

Correct answer:

Explanation:

Based on the power rule for exponents we can write:

$(a^m)^{n}=a^{m\times n}$

这意味着;提高电力我们需要权力multiply the exponents. So we can write:

$\frac{3x^{\sqrt{2}}(x^{\sqrt{3}})^\sqrt{3}}{x^{\sqrt{2}}}=3\times \left(\frac{x^{\sqrt{2}}}{x^{\sqrt{2}}}\right) \times (x^{\sqrt{3}})^{\sqrt{3}}=3x^{\sqrt{3}\times \sqrt{3}}=3x^3$

Substitute x=2 and we get:

$3x^3=3\times 2^3=3\times 8=24$

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Example Question #22 :Exponents

Simplify:

$(x^{2\sqrt{2}})^{3\sqrt{2}}$

Possible Answers:

$x^{12}$

$x^{8}$

$x^{6}$

$x^{6\sqrt{}2}$

$x^{2}$

Correct answer:

$x^{12}$

Explanation:

Based on the power rule, we know that in order to raise a power to a power we need to multiply the exponents, i.e.

$(x^{m})^{n}=x^{m\times n}$ .

$(x^{2\sqrt{2}})^{3\sqrt{2}}=x^{2\sqrt{2}\times 3\sqrt{2}}=x^{2\times 3\times 2}=x^{12}$

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Example Question #23 :Exponents

Simplify:

$(\frac{12x^{3}}{3x^{-1}})^{4}$

Possible Answers:

$256x^{12}$

$16x^{8}$

$256x^{8}$

$256x^{16}$

$16x^{16}$

Correct answer:

$256x^{16}$

Explanation:

The Negative Exponent Rule says $a^{-n}=\frac{1}{a^n}$ .

$(\frac{12x^{3}}{3x^{-1}})^{4}=(\frac{12}{3}\times x^{3+1})^{4}=(4x^4)^{4}$

The power rule says that, in order to raise a power to a power, we need to multiply the exponents, i.e. $(x^{m})^{n}=x^{m\times n}$ .

$(\frac{12x^{3}}{3x^{-1}})^{4}=(4x^4)^{4}=4^4\times x^{4\times 4}=256x^{16}$

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Example Question #24 :Exponents

What is the value of this equation?

$(x^{2})^{3}-(2^{3})^{2}$

Possible Answers:

$x^{5}-64$

$x^{6}-32$

$x^{6}-64$

$x^{6}+64$

Correct answer:

$x^{6}-64$

Explanation:

When an exponent is raised to another exponent, the exponents should be multiplied toghether. This will result in:

$(x^{2})^{3}-(2^{3})^{2}$

$x^{6}-2^{6}$

$x^{6}-64$

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Example Question #25 :Exponents

Which expression is equal to $(x^{2})^{3}$ ?

Possible Answers:

$x^{5}$

$x^{\frac{2}{3}}$

$x^{6}$

$x^{\frac{3}{2}}$

Correct answer:

$x^{6}$

Explanation:

When exponent of a value is raised to another exponent, the values of the exponents are multiplied by each other.

$(x^{2})^{3}$

2 is multiplied by 3, and so the exponent of x is 6.

$x^{6}$

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Example Question #26 :Exponents

What is the value of $(2^{6})^{\frac{1}{2}}$ ?

Possible Answers:

Correct answer:

Explanation:

When one exponent is raised to another exponent, the values of the exponents should be multiplied together. Thus,

$(2^{6})^{\frac{1}{2}}$ can be simplified to $2^{3}$ , given that $6\cdot \frac{1}{2}=3$ .

$2^{3}=2\cdot2\cdot2=8$

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Example Question #27 :Exponents

What is the expression below equal to?

$3x^{4}*5x^{9}$

Possible Answers:

$15x^{13}$

$8x^{9}$

$15x^{36}$

$8x^{36}$

Correct answer:

$15x^{13}$

Explanation:

When exponents are multiplied by each other, the powers should be added together. Meanwhile, numbers not raised to an exponent are simply multiplied by each other.

Therefore, the answer is $15x^{13}$ , because 3*5=15 , and 9+4=13 .

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Example Question #28 :Exponents

What is the value of $-1^{323}$ ?

Possible Answers:

323

Correct answer:

Explanation:

1 raised to any exponent will always be 1.

-1 will be equal to 1 when the exponent is even and will be equal to -1 when the exponent is odd.

Given that 323 is odd, $-1^{323}$ is equal to -1.

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Example Question #29 :Exponents

Simplify the following:

6x^5*5x^6*3x^2

Possible Answers:

$90x^{13}$

$14x^{90}$

$45x^{7}$

$33x^{11}$

Correct answer:

$90x^{13}$

Explanation:

Simplify the following:

6x^5*5x^6*3x^2

Let's begin by recalling two rules

1) When multiplying variables with a common base, add the exponents.

2) When multiplying variables with a common base, multiply the coefficients.

$6x^5*5x^6*3x^2=(5*6*3)x^{5+6+2}=90x^{13}$

So, our answer is

$90x^{13}$

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Example Question #30 :Exponents

Simplify: $\frac{12x^{12}}{3x^{3}}$

Possible Answers:

$9x^{9}$

$\frac{4}{x^{9}}$

$\frac{x^{9}}{4}$

$4x^{4}$

$4x^{9}$

Correct answer:

$4x^{9}$

Explanation:

Separate the fraction and apply the quotient of powers rule:

$\frac{12x^{12}}{3x^{3}} = \frac{12}{3} \cdot \frac{x^{12}}{x^{3}} = 4x^{12-3} = 4x^{9}$

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ISEE Upper Level Math : Exponents

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 :How To Multiply Exponents

Example Question #22 :Exponents

Example Question #23 :Exponents

Example Question #24 :Exponents

Example Question #25 :Exponents

Example Question #26 :Exponents

Example Question #27 :Exponents

Example Question #28 :Exponents

Example Question #29 :Exponents

Example Question #30 :Exponents

All ISEE Upper Level Math Resources

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