An algebra problem by A Former Brilliant Member

Algebra Level 1

5 4 × 5 − 2 = ? 5^4 \times 5^{-2} = \, ?

25 15 10 20

A Former Brilliant Member by A Former Brilliant Member

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4 solutions

Mohammad Khaza
Jul 5, 2017

5^4 x 5^-2

= 5^4 x 1/5^2

= (5 x 5 x 5 x 5) / (5 x 5)

=5^2=25

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Sathvik Acharya
Jun 10, 2017

5 4 × 5 − 2 = 5 4 × 1 5 2 = 5 4 5 2 = 5 4 − 2 = 5 2 = 25 5^4\times 5^{-2}=5^4\times \frac{1}{5^2}=\frac{5^4}{5^2}=5^{4-2}=5^{2}=\boxed{25}

Laws of exponents used:

  • a − b = 1 a b a^{-b}=\dfrac{1}{a^b}

  • a x a y = a x − y \dfrac{a^{x}}{a^{y}}=a^{x-y}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

=5^4/5^2 =5^4+2 =5^4-2 =5^2 =25

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Jacob, use L a T e X L_aT^eX here too.

Peter Michael - 3 years, 12 months ago
Peter Michael
Jun 9, 2017

Power laws for same base

The sum of the exponents

Evaluate it

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