Question

negative exponent and zero exponent properties

1. $a^{-7} = $
2. $(21c^{18})^{-1} = $
3. $(3d^2)^0 = $
4. $5(x^0)y^{-1} = $

Explanation:

Step1: Apply negative exponent rule

$a^{-n}=\frac{1}{a^n}$, so $a^{-7}=\frac{1}{a^7}$

Step2: Apply negative exponent to product

$(21c^{18})^{-1}=\frac{1}{21c^{18}}$

Step3: Apply zero exponent rule

Any non-zero term to 0 power is 1, so $(3d^2)^0=1$

Step4: Simplify zero and negative exponents

First, $x^0=1$, then $y^{-1}=\frac{1}{y}$. So $5(x^0)y^{-1}=5\times1\times\frac{1}{y}=\frac{5}{y}$

Answer:

1. $\frac{1}{a^7}$
2. $\frac{1}{21c^{18}}$
3. $1$
4. $\frac{5}{y}$