Question

Simplify each fraction.

a) 2³×2⁴/2⁵
b) a³×a²/a²
c) d³×d/d¹
d) 10⁶×10⁴/10²×10³


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Answer 1

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$\sf{a) \dfrac{ {2}^{3} \times {2}^{4} }{ {2}^{5} } }$

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$\qquad : \implies \sf{ \dfrac{ {2}^{3} \times {2}^{4} }{ {2}^{5} } }$

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$\qquad : \implies \sf{ \dfrac{ {2}^{3 + 4} }{ {2}^{5} } }$

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$\qquad : \implies \sf{ \dfrac{ {2}^{7} }{ {2}^{5} } }$

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$\qquad : \implies { {2}^{7 - 5} }$

$\qquad : \implies{ {2}^{2} }$

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$\sf{b) \dfrac{ {a}^{3} \times {a}^{2} }{ {a}^{2} } }$

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$\qquad : \implies \sf{ \dfrac{ {a}^{3 + 2} }{ {a}^{2} } }$

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$\qquad : \implies \sf{ \dfrac{ {a}^{5} }{ {a}^{2} } }$

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$\qquad : \implies \sf{ {a}^{5 - 2} }$

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$\qquad : \implies \sf{ {a}^{3} }$

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$\sf{c) \dfrac{ {d}^{3} \times d }{ {d}^{1} } }$

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$\qquad : \implies \sf{ \dfrac{ {d}^{3 + 1} }{ {d}^{1} } }$

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$\qquad : \implies \sf{ \dfrac{ {d}^{4} }{ {d}^{1} } }$

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$\qquad : \implies \sf{ {d}^{4 - 1} }$

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$\qquad : \implies \sf{ {d}^{3} }$

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$\sf{d) \dfrac{ {10}^{6} \times {10}^{4} }{ {10}^{2} \times {10}^{3} } }$

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$\qquad : \implies \sf{ \dfrac{ {10}^{6 + 4} }{ {10}^{2 + 3} } }$

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$\qquad : \implies{ \dfrac{ {10}^{10} }{ {10}^{5} } }$

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$\qquad : \implies{ {10}^{10 - 5} }$

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$\qquad : \implies{ {10}^{5} }$

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