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Apply the exponent rule a^m x aⁿ = a^m+n.

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4 parts
e

243\text{243}

f

16\text{16}

g

36\text{36}

h

1\text{1}

Step-by-step solution

12 steps

Here are the calculations for the next set of problems, assuming they are parts e, f, g, and h based on the previous question:

Part e· 3 steps

Calculate 32×333^2 \times 3^3

  1. Apply the exponent rule am×an=am+na^m \times a^n = a^{m+n}.

    32×33=32+33^2 \times 3^3 = 3^{2+3}

  2. Add the exponents.

    32+3=353^{2+3} = 3^5

  3. Expand and multiply.

    35=3×3×3×3×3=2433^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243

    The value is 243\boxed{\text{243}}.

Part f

16\text{16}

Calculate 45÷434^5 \div 4^3

  1. Apply the exponent rule am÷an=am−na^m \div a^n = a^{m-n}.

    45÷43=45−34^5 \div 4^3 = 4^{5-3}

  2. Subtract the exponents.

    45−3=424^{5-3} = 4^2

  3. Expand and multiply.

    42=4×4=164^2 = 4 \times 4 = 16

    The value is 16\boxed{\text{16}}.

Part g

36\text{36}

Calculate 22×322^2 \times 3^2

  1. Apply the exponent rule am×bm=(a×b)ma^m \times b^m = (a \times b)^m.

    22×32=(2×3)22^2 \times 3^2 = (2 \times 3)^2

  2. Multiply the bases.

    (2×3)2=62(2 \times 3)^2 = 6^2

  3. Expand and multiply.

    62=6×6=366^2 = 6 \times 6 = 36

    The value is 36\boxed{\text{36}}.

Part h

1\text{1}

Calculate 53÷535^3 \div 5^3

  1. Apply the exponent rule am÷an=am−na^m \div a^n = a^{m-n}.

    53÷53=53−35^3 \div 5^3 = 5^{3-3}

  2. Subtract the exponents.

    53−3=505^{3-3} = 5^0

  3. Any non-zero number raised to the power of 0 is 1.

    50=15^0 = 1

    The value is 1\boxed{\text{1}}.

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