Question

1) Use the rules of exponents to evaluate or simplify. Write without negative exponents.
3*4^0 = ____

2) Use the rules of exponents to evaluate or simplify. Write without negative exponents.
1 / 4^-2 = ____

Answer 1

1) 3*4^0 = 3*1 =3
2) 1/4 ^-2 = 16

Answer 2

Answer:

Given that:

i) $3\times 4^0$

The value of $a^0=1$

The power zero of anything is equal to one.

$4^0=1\\\\3 \times 1=3\\\\\therefore 3 \times 4^0 = 3 \times 1\\\\3 \times 4^0=3.$

Therefore, the value of $3 \times 4^0$ is 3.

II) $\frac{1}{4^{-2}}$

The value of $a^{-2}=\frac{1}{a^{2}}$

$\begin{array} { l } { 4 ^ { - 2 } = \frac { 1 } { 4 ^ { 2 } } } \\\\ { = \frac { 1 } { 16 } } \\ { 4 ^ { - 2 } = \frac { 1 } { 16 } } \\\\ { \frac { 1 } { 4 ^ { - 2 } } = \frac { 1 } { \left( \frac { 1 } { 16 } \right) } } \\\\ { = 1 \times \frac { 16 } { 1 } } \\\\ { \therefore \frac { 1 } { 4 ^ { - 2 } } = 16 } \end{array}$

Therefore, the value of $\frac{1}{4^{-2}}$ is 16.