# What I learned this week

This week, I learned about the exponents laws, and here are some of them:

Rule: When multiplying powers with the same base, you add the exponents.

1) $5^3$$5^4$ = $5^7$

5•5•5•5•5•5•5= $5^7$

2) $3^3$$3^2$ = $3^5$

3•3•3•3•3= $3^5$

Rule: When dividing powers with the same base, you subtract the exponents.

1) $5^5$ ÷ $5^3$ = $5^2$

2) $5^7$ ÷ $5^4$ = $5^3$

Rule: To raise a power to a power, multiply the exponents.

Rule: When a product is raised to an exponent, you can rewrite each factor in the product with the same exponent.

( 3 × 2 ) $^3$

( 3 × 2 ) ( 3 × 2 ) ( 3 × 2 ) = $3^2$$2^3$

Rule: When a quotient is raised to an exponent, you can rewrite each number in the quotient with the same exponent.

1) $5^4$ ÷ $5^4$ = $5^0$ = 1

Rule: When the exponent of a power is zero, the value of the power is 1 (as long as the base is zero)

[ 2× ( -3 ) ] $^5$

= $2^5$$(-3)^5$

= -7776