Properties of Exponents and Rational Exponents

Front

Anything raised to a power of zero is always:

Back

1

Front

Simplify (3x^3y^5)^4

Back

81x^{12}y^{20}

Front

Write as a rational exponent: n^3

Back

n^{rac{3}{1}}

Front

Write as a rational exponent: n^{rac{3}{2}}

Back

n^{rac{3}{2}}

Front

Write as a rational exponent: 2^{rac{n}{3}}

Back

2^{rac{n}{3}}

Front

Write as a rational exponent: n^{rac{1}{3}}

Back

n^{rac{1}{3}}

Front

Simplify the expression: (6x^{-1}y^{3})^3

Back

216x^{-3}y^{9}

Front

What is the product of powers property?

Back

When multiplying two powers with the same base, add the exponents: a^m * a^n = a^{m+n}.

Front

What is the power of a power property?

Back

When raising a power to another power, multiply the exponents: (a^m)^n = a^{m*n}.

Front

What is the power of a product property?

Back

When raising a product to a power, apply the exponent to each factor: (ab)^n = a^n * b^n.