Boost your exponent skills! In this video, we'll simplify expressions and write them in exponential form. We'll tackle a variety of problems, including fractions, negative exponents, and combined operations. Perfect for algebra students!
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𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧: Write in exponential form (2⁴ x 2 x 7³ x 7⁶) / (2³ x 7⁴)
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
Using the rules of exponents:
a^m × a^n = a^(m+n)
a^m / a^n = a^(m-n)
Simplify the numerator:
2⁴ × 2 = 2^(4+1) = 2⁵
7³ × 7⁶ = 7^(3+6) = 7⁹
Numerator = 2⁵ × 7⁹
Now, divide by the denominator:
(2⁵ × 7⁹) / (2³ × 7⁴) = (2⁵ / 2³) × (7⁹ / 7⁴)
= 2^(5-3) × 7^(9-4)
= 2² × 7⁵
Exponential form: 2² × 7⁵