Laws of Exponents: Power of a Power

Front

What is the Power of a Power rule in exponents?

Back

When raising a power to another power, you multiply the exponents. For example, (a^m)^n = a^(m*n).

Front

Simplify: (x^3)^4

Back

x^(3*4) = x^12.

Front

What does it mean to simplify (2x)^3?

Back

It means to expand it as (2x)(2x)(2x) = 8x^3.

Front

If a^m * a^n = ?

Back

a^(m+n). This is the product of powers rule.

Front

What is the result of (3y^4)^2?

Back

9y^8, because (3^2)(y^(4*2)) = 9y^8.

Front

How do you simplify (4xy^4)^3?

Back

64x^3y^12, because (4^3)(x^3)(y^(4*3)) = 64x^3y^12.

Front

What is the quotient of powers rule?

Back

When dividing powers with the same base, subtract the exponents: a^m / a^n = a^(m-n).

Front

Simplify: (x^2y^3)^5

Back

x^(2*5)y^(3*5) = x^10y^15.

Front

What is the result of (ab)^3?

Back

a^3b^3, because you distribute the exponent to both a and b.

Front

If (x^2)^3 = ?

Back

x^(2*3) = x^6.