Algebra II - Multiplying and Dividing Exponents

Evaluate:

$15^{11}$

$15^{28}$

$225^{11}$

$225^{28}$

$30^{11}$

Explanation

When multiplying exponents with same base, we just add the exponents and keep the base the same.

$15^4*15^7=15^{4+7}=15^{11}$

Simplify $x^3x^{-4}x^7$

Explanation

Combine all like variables. We only have the variable 'x', so we can skip that step. to multiply or divide exponents, you add, so you get 3 + (-4) + 7 = 6. The answer is

Divide: $\frac{25^{30}}{5^{90}}$

$\frac{1}{5^{30}}$

$5^{30}$

$25^{3}$

$\frac{1}{25^{3}}$

$\frac{1}{5^{60}}$

Explanation

Change the base of the numerator so that it matches the denominator.

We can rewrite the numerator as five squared.

$\frac{25^{30}}{5^{90}} = \frac{(5^2)^{30}}{5^{90}}$

Use the product rule of exponents to simplify the numerator.

$\frac{(5^2)^{30}}{5^{90}} = \frac{5^{60}}{5^{90}}$

Subtract the powers.

$5^{60-90} = 5^{-30}$

Rewrite the negative exponent as a fraction.

The answer is: $\frac{1}{5^{30}}$

Simplify:

$x^{11}$

$2x^{11}$

$x^{30}$

$2x^{30}$

$x^{12}$

Explanation

When multiplying exponents with the same base, we just keep the base the same and add the exponents.

$x^5*x^6=x^{5+6}=x^{11}$

Simplify:

$23^{15}$

$23^{56}$

$23^{9}$

$23^{10}$

$23^{19}$

Explanation

When multiplying exponents with the same base, we add the exponents and keep the base the same.

$23^7*23^8=23^{7+8}=23^{15}$

Simplify: $10^7*10^{12}$

$10^{19}$

$10^{84}$

$10^{34}$

$10^{29}$

$10^{9}$

Explanation

When multiplying exponents with the same base, we just add the exponents and keep the base the same.

$10^7*10^{12}=10^{7+12}=10^{19}$

Simplify:

$8^{16}$

$8^{64}$

$64^{16}$

$64^{64}$

Explanation

When exponents with the same base are multiplied together, we we will simply add the exponents and keep the base the same.

Multiply:

$8^8*8^8=8^{8+8}=8^{16}$

Simplify: $15^8*15^{12}$

$15^{20}$

$15^{96}$

$15^{24}$

$225^{20}$

$225^{96}$

Explanation

When multiplying exponents with the same base, we just add the exponents and keep the base the same.

$15^8*15^{12}=15^{8+12}=15^{20}$

Simplify.

$\frac{x^5}{x^4}$

$x^{1.25}$

$x^{20}$

$x^{-1}$

Explanation

When dividing exponents, we must first check to see if the factors have the same base. If they have the same bases, then we can subtract the exponents.

$\frac{x^5}{x^4}=x^{5-4}$