How to multiply exponents

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SAT Math › How to multiply exponents

Questions 1 - 10

1

Simplify:

$4^7*4^{18}$

$4^{25}$

$4^{126}$

$4^{35}$

$4^{45}$

$4^{106}$

Explanation

When multiplying exponents, we just add the exponents while keeping the base the same.

$4^7*4^{18}=4^{7+18}=4^{25}$

2

$2^{12}$

Explanation

When multplying exponents, we need to make sure we have the same base.

Since we do, all we have to do is add the exponents.

The answer is $2^{3+4}=2^7$ .

3

Solve:

$x^{2}\cdot x$

$x^{3}$

$x^{2}$

$x^{5}$

Explanation

When multiplying expressions with the same variable, combine terms by adding the exponents, while leaving the variable unchanged. For this problem, we do that by adding 2+1, to get a new exponent of 3:

$x^{2}\cdot x=x ^{2+1}=x^{3}$

4

$3^4*3^{15}*3^2$

$3^{21}$

$3^{15}-2$

$3^{20}+2$

Explanation

When multplying exponents, we need to make sure we have the same base.

Since we do, all we have to do is add the exponents.

The answer is $3^{4+15+2}=3^{21}$ .

5

Simplify the expression.

Explanation

When multiplying with exponents, you must add the exponents.

Therefore, multiply the coefficients on the x terms and add the exponents

$\1x^3\cdot2x^2=2x^(3+2)=2x^5$

6

Simplify:

$12^{16}$

$35^{16}$

Explanation

When multiplying exponents with different bases but the same exponent, you multiply the bases and keep the exponents the same.

7

Solve:

$x\cdot x^{3}$

$x^{4}$

$x^{2}$

$x^{3}$

$x^{5}$

Explanation

When multiplying expressions with the same variable, combine terms by adding the exponents, while leaving the variable unchanged. For this problem, we do that by adding 3+1, to get a new exponent of 4:

$x^{3}\cdot x=x ^{3+1}=x^{4}$

8

(b * b4 * b7)1/2/(b3 * bx) = b5

If b is not negative then x = ?

–2

–1

7

1

Explanation

Simplifying the equation gives b6/(b3+x) = b5.

In order to satisfy this case, x must be equal to –2.

9

$6^{24}$

$6^{504}$

$6^{65}$

$6^{-8}$

$6^{-1}$

Explanation

When multplying exponents, we need to make sure we have the same base.

Since we do, all we have to do is add the exponents.

The answer is $6^{7+8+9}=6^{24}$ .

10

Convert the product of to base .

$2^{36}$

$2^{24}$

$2^{12}$

$2^{16}$

$2^{64}$

Explanation

Although they have different bases, we know that .

Therefore

$16^8=(2^4)^8=2^{32}$ .

Remember to apply the power rule of exponents.

Finally,

$2^{32}*2^4=2^{32+4}=2^{36}$ .

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