8.EE.A.1 Tutor Intake -- Properties of Integer Exponents

$4^6$

$4^5$

$4^1$

$4^{3 \cdot 2}$

$2^3 \cdot 2^4$ multiplies the exponents; $(2^3)^4$ adds the exponents.

Both expressions multiply their exponents, since both involve exponents and multiplication somewhere in the expression.

$2^3 \cdot 2^4$ adds the exponents (two separate powers multiplied); $(2^3)^4$ multiplies the exponents (one power raised to another power).

Both expressions add their exponents, since both are built from the same base, 2.

$5^0 = 1$, because $5 \div 5 = 1$.

$5^0 = 0$, because raising to the zero power means "zero copies," which is nothing.

$5^0 = 5$, because the pattern stays the same once the exponent reaches zero.

$5^0$ is undefined, because you can't raise a number to the power of zero.

Positive; $2^{-3} = 1/8$.

Negative; $2^{-3} = -8$.

Negative; $2^{-3} = -1/8$.

Positive; $2^{-3} = 8$.