Question

1. 18⁵=____
2. t⁰=____
3. (3)⁴=____
4. 5⁻³=____
5. p⁻⁴=____
6. 10⁷=____

(the text on the right: delete each exponent)

Explanation:

Step1: Recall exponent rules

For any non - zero number \(a\), \(a^{0}=1\) (zero - exponent rule), and \(a^{-n}=\frac{1}{a^{n}}\) (negative - exponent rule).

Step2: Solve \(18^{0}\)

Using the zero - exponent rule (\(a^{0} = 1\) for \(a
eq0\)), since \(18
eq0\), \(18^{0}=1\).

Step3: Solve \(t^{0}\)

Using the zero - exponent rule, for \(t
eq0\), \(t^{0}=1\). If \(t = 0\), \(0^{0}\) is undefined, but generally in the context of exponent rules, we assume \(t
eq0\), so \(t^{0}=1\).

Step4: Solve \((3)^{4}\)

\((3)^{4}=3\times3\times3\times3 = 81\).

Step5: Solve \(5^{-3}\)

Using the negative - exponent rule \(a^{-n}=\frac{1}{a^{n}}\), here \(a = 5\) and \(n = 3\), so \(5^{-3}=\frac{1}{5^{3}}=\frac{1}{125}\).

Step6: Solve \(p^{-4}\)

Using the negative - exponent rule, \(p^{-4}=\frac{1}{p^{4}}\) (assuming \(p
eq0\)).

Step7: Solve \(10^{7}\)

\(10^{7}=10\times10\times10\times10\times10\times10\times10 = 10000000\).

Answer:

s:

1. \(18^{0}=\boldsymbol{1}\)
2. \(t^{0}=\boldsymbol{1}\) (for \(t

eq0\))

1. \((3)^{4}=\boldsymbol{81}\)
2. \(5^{-3}=\boldsymbol{\frac{1}{125}}\)
3. \(p^{-4}=\boldsymbol{\frac{1}{p^{4}}}\) (for \(p

eq0\))

1. \(10^{7}=\boldsymbol{10000000}\)