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First, let's note that 27 is a power of the number 3:
Using this fact gives us a situation where in the fraction's numerator and denominator we get terms with identical bases, let's apply this to the problem:
Now let's recall the law of exponents for division between terms without identical bases:
Let's apply this law to the last expression we got:
where in the first stage we applied the above law and in the second stage we simplified the expression we got in the exponent,
Let's summarize the solution steps, we got:
Therefore the correct answer is answer D.
\( 112^0=\text{?} \)
Think of powers of 3: 3¹ = 3, 3² = 9, 3³ = 27. You can also work backwards: what number times itself three times gives 27? That's 3 × 3 × 3 = 27!
When the bottom exponent is larger than the top exponent, you get a negative result. Here: 3 - 8 = -5. Negative exponents mean "one over" the positive power.
. The negative exponent tells you to flip it to a fraction with 1 on top and the positive power on bottom.
You could calculate directly, but using exponent laws is much faster and less prone to arithmetic errors!
Convert both forms to decimals: and . Same result means you're right!
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