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SAT Math : Exponential Operations

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Example Questions

Example Question #151 : Exponential Operations

Solve:

$\frac{x^{\frac{3}{4}}}{x^{\frac{1}{4}}}$

Possible Answers:

$\frac{1}{x}$

$\frac{1}{x^{2}}$

$x^{\frac{1}{2}}$

$x^{2}$

Correct answer:

$x^{\frac{1}{2}}$

Explanation:

$\frac{x^{\frac{3}{4}}}{x^{\frac{1}{4}}}=x ^{\frac{3}{4}-\frac{1}{4}}=x^{\frac{2}{4}}=x^{\frac{1}{2}}$

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Example Question #152 : Exponential Operations

Solve:

$\frac{x^{\frac{3}{5}}}{x^{\frac{2}{5}}}$

Possible Answers:

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

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

$x^{\frac{1}{5}}$

Correct answer:

$x^{\frac{1}{5}}$

Explanation:

$\frac{x^{\frac{3}{5}}}{x^{\frac{2}{5}}}=x ^{\frac{3}{5}-\frac{2}{5}}=x^{\frac{1}{5}}$

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Example Question #41 : How To Divide Exponents

Solve:

$\frac{x^{3}}{x^{5}}$

Possible Answers:

$\frac{1}{x^{10}}$

$x^{8}$

$x^{2}$

$\frac{1}{x^{2}}$

Correct answer:

$\frac{1}{x^{2}}$

Explanation:

When dividing expressions with the same variable, combine terms by subtracting the exponents, while leaving the variable unchanged. For this problem, we do that by subtracting 3-5, to get a new exponent of -2. However, because the exponent is negative, we can place the new expression in the denominator of the fraction and make the exponent positive:

$\frac{x^{3}}{x^{5}}=^{3-5}=x^{-2}=\frac{1}{x^{2}}$

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Example Question #42 : How To Divide Exponents

Solve:

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

Possible Answers:

$\frac{1}{x^{8}}$

$\frac{1}{x^{2}}$

$\frac{1}{x^{4}}$

$x^{4}$

Correct answer:

$\frac{1}{x^{4}}$

Explanation:

When dividing expressions with the same variable, combine terms by subtracting the exponents, while leaving the variable unchanged. For this problem, we do that by subtracting 2-6, to get a new exponent of -4. However, because the exponent is negative, we can place the new expression in the denominator of the fraction and make the exponent positive:

$\frac{x^{2}}{x^{6}}=^{2-6}=x^{-4}=\frac{1}{x^{4}}$

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Example Question #43 : How To Divide Exponents

Solve:

$\frac{x^{11}}{x^{16}}$

Possible Answers:

$\frac{1}{x^{5}}$

$x^{27}$

$\frac{1}{x^{-5}}$

$x^{5}$

Correct answer:

$\frac{1}{x^{5}}$

Explanation:

When dividing expressions with the same variable, combine terms by subtracting the exponents, while leaving the variable unchanged. For this problem, we do that by subtracting 11-16, to get a new exponent of -5. However, because the exponent is negative, we can place the new expression in the denominator of the fraction and make the exponent positive:

$\frac{x^{11}}{x^{16}}=^{11-16}=x^{-5}=\frac{1}{x^{5}}$

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Example Question #44 : How To Divide Exponents

Simplify:

$\frac{4^{44}}{4^{26}}$

Possible Answers:

$4^{18}$

$4^{58}$

$4^{66}$

$4^{32}$

$4^{72}$

Correct answer:

$4^{18}$

Explanation:

When dividing exponents, we subtract the exponents and keep the base the same.

$\frac{4^{44}}{4^{26}}=4^{44-26}=4^{18}$

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Example Question #45 : How To Divide Exponents

Simplify: $\frac{5^{18}}{5^{-18}}$

Possible Answers:

$\frac{1}{5}$

$5^{-36}$

$5^{36}$

Correct answer:

$5^{36}$

Explanation:

When dividing exponents, we subtract the exponents and keep the base the same.

$\frac{5^{18}}{5^{-18}}=5^{18-(-18)}=5^{36}$

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Example Question #46 : How To Divide Exponents

Simplify:

$\frac{36^5}{6^{19}}$

Possible Answers:

$6^{9}$

6^7

$6^{-14}$

$6^{-9}$

$6^{12}$

Correct answer:

$6^{-9}$

Explanation:

Although the bases aren't the same, we know that 36=6^2 .

Therefore

$36^5=(6^2)^5=6^{10}$ .

We can now divide the exponents.

$6^{10}\div6^{19}=6^{10-19}=6^{-9}$

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Example Question #2 : Exponential Operations

$\dpi{100} \small \frac{7^{10}-7^{8}}{7^{9}-7^{7}}=$

Possible Answers:

$\dpi{100} \small 28$

$\dpi{100} \small 49$

$\dpi{100} \small 343$

$\dpi{100} \small 42$

$\dpi{100} \small 7$

Correct answer:

$\dpi{100} \small 7$

Explanation:

The easiest way to solve this is to simplify the fraction as much as possible. We can do this by factoring out the greatest common factor of the numerator and the denominator. In this case, the GCF is 7^7 .

$\frac{7^7\left ( 7^3-7^1\right)}{7^7\left ( 7^2-1\right)}$

Now, we can cancel out the 7^7 from the numerator and denominator and continue simplifying the expression.

$\frac{7^7\left ( 7^3-7^1\right)}{7^7\left ( 7^2-1\right)}=\frac{7^3-7^1}{7^2-1}=\frac{343-7}{49-1}=\frac{336}{48}=7$

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Example Question #570 : Algebra

$\frac{x^a}{x^b}=x^4$

and

3a + b = 20 ,

what is the value of a?

Possible Answers:

$\frac{80}{13}$

Correct answer:

Explanation:

When dividing exponents,

$\frac{x^a}{x^b}=x^{a-b}$ .

Therefore,

$x^{a-b}=x^4$ .

If $x^{a-b}= x^4$ , then a-b=4 .

We can now solve the system of equations a-b=4 and 3a + b= 20 .

If we solve for a in the first equation and plug it into the second equation, we get 3(4-b)+ b=20 and find the value of b to be .

If we substitute this value of b into the first equation, we can solve for a and find that a=6 .

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SAT Math : Exponential Operations

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #151 : Exponential Operations

Example Question #152 : Exponential Operations

Example Question #41 : How To Divide Exponents

Example Question #42 : How To Divide Exponents

Example Question #43 : How To Divide Exponents

Example Question #44 : How To Divide Exponents

Example Question #45 : How To Divide Exponents

Example Question #46 : How To Divide Exponents

Example Question #2 : Exponential Operations

Example Question #570 : Algebra

All SAT Math Resources

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