Powers with the Same Base

Complete the rules.

$$\left(x^m\right)^n=$$ ​ (a)   , $$x^m\cdot x^n=$$ ​ ​ (b)  

$$\frac{x^m}{x^n}=$$ ​ (c)   , $$\frac{x^n}{x^m}=$$ ​ (d)  

Match the following expressions with the equivalent single power.

What value of $$n$$ makes the equation true?

$$\frac{\left(-5\right)^{11}}{\left(-5\right)^n}=\left(-5\right)^2\cdot\left(-5\right)^1$$

Hint: If each side were rewritten as a single power, what would the missing value need to be to get both sides to match?

What value of x makes the equation true?

$$\left(x^4\right)^2=7^8$$

What is the value of the expression $$\frac{3^5\cdot3^4}{\left(3^2\right)^3}$$ ?

(Value means standard form!)

Rewrite the expression as a single power.

(Use ^ to form an exponent)

$$\frac{2^9}{2^5}$$

When you multiply two powers with the same base you can ​ (a)   the exponents.

When you divide two powers with the same base you can ​ (b)   the exponents.