Solve: 5³ + 5⁻³ × 5³ Expression with Mixed Exponents

Question

53+5−3⋅53=? 5^3+5^{-3}\cdot5^3=\text{?}

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 When multiplying powers with equal bases
00:08 The power of the result equals the sum of the powers
00:12 We'll apply this formula to our exercise, and proceed to add the powers together
00:23 According to the laws of powers, any number raised to the power of 0 equals 1
00:27 As long as the number is not 0
00:30 We'll apply this formula to our exercise
00:33 This is the solution

Step-by-Step Solution

We'll use the power rule for multiplication between terms with identical bases:

am⋅an=am+n a^m\cdot a^n=a^{m+n} and we'll simplify the second term on the left in the equation using it:
53+5−3⋅53=53+5−3+3=53+50=53+1 5^3+5^{-3}\cdot5^3=5^3+5^{-3+3}=5^3+5^0=5^3+1 where in the first stage we applied the mentioned rule to the second term on the left, then we simplified the expression with the exponent, and in the final stage we used the fact that any number raised to the power of 0 equals 1,

We didn't touch the first term of course since it was already simplified,

Therefore the correct answer is answer C.

Answer

53+1 5^3+1

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Related Subjects

Zero Exponent Rule Exponents and Exponent rules Rules of Exponentiation Combining Powers and Roots Properties of Exponents Exponents - Special Cases

Question Types

Zero Exponent Rule: Using the laws of exponents Applying Combined Exponents Rules: Using the laws of exponents Applying Combined Exponents Rules: Calculating powers with negative exponents Applying Combined Exponents Rules: Monomial Applying Combined Exponents Rules: A power law