Introduction to Exponents: Practice

The parentheses make $-2$ the base, and four negative factors multiply to a positive.

$(-2)^4 = (-2)(-2)(-2)(-2) = 16$

An even number of negative factors gives a positive result.

Without parentheses the exponent applies only to the $2$, and the minus sign comes after.

$-2^4 = -(2^4) = -16$

Compare with $(-2)^4 = 16$, where the parentheses make $-2$ the base.

Compute each value, then compare.

$2^{10} = 1024, \quad 10^2 = 100, \quad 3^5 = 243, \quad 5^3 = 125$

The largest is $2^{10} = 1024$.

Doubling $6$ times multiplies by $2$ six times.

$2^6 = 64$

It is not $6 \times 2 = 12$; the count of doublings is the exponent.

Evaluate each power separately, then multiply the results.

$2^3 = 8, \quad 5^2 = 25, \quad 8 \times 25 = 200$

Compute each value.

$16^2 = 256, \qquad 2^{16} = 65{,}536$

So $2^{16}$ is far greater. Here the exponent matters much more than the base.

Power first, then multiplication, then subtraction.

$6^2 = 36, \quad 36 \times 2 = 72, \quad 100 - 72 = 28$

Multiply $3$'s until you reach $81$.

$3 \times 3 \times 3 \times 3 = 81$

That is four factors, so $x = 4$.

Evaluate each power, then multiply the results.

$2^2 = 4, \quad 2^3 = 8, \quad 4 \times 8 = 32$

Compute each value.

$3^3 = 27, \quad 2^5 = 32, \quad 6^2 = 36, \quad 4^2 = 16$

The largest is $6^2 = 36$.

Power first, then multiplication, then addition.

$4^2 = 16, \quad 2 \times 16 = 32, \quad 5 + 32 = 37$

Evaluate each power, then subtract.

$10^3 = 1000, \quad 10^2 = 100, \quad 1000 - 100 = 900$

It is not $10^{3-2} = 10$; subtract the values, not the exponents.