simplifying exponents and rewriting rational exponents and radicals

Front

What is the product of powers property of exponents?

Back

When multiplying two expressions with the same base, add the exponents: a^m ⋅ a^n = a^(m+n).

Front

What is the power of a power property of exponents?

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 of exponents?

Back

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

Front

What is the zero exponent rule?

Back

Any non-zero base raised to the power of zero equals one: a^0 = 1 (where a ≠ 0).

Front

What is the negative exponent rule?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: a^(-n) = 1/(a^n).

Front

How do you simplify (x^3 ⋅ y^4 ⋅ z)^3 ⋅ (x^5 ⋅ y ⋅ z^3)^2?

Back

x^19 ⋅ y^14 ⋅ z^9.

Front

What is the definition of a rational exponent?

Back

A rational exponent is an exponent that is a fraction, representing both a power and a root: a^(m/n) = n√(a^m).

Front

How do you rewrite a radical in exponential form?

Back

The nth root of a number can be expressed as a fractional exponent: n√(a) = a^(1/n).

Front

What is the simplified form of (5^3 x^2 y^4)^0?

Back

1.

Front

What is the simplified form of 10x^(-2)?

Back

10/x^2.