Which is larger?
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Which is larger?
Let's address the problem by evaluating each expression separately:
Step 1: Evaluate .
Here, the expression represents the negative of . The correct interpretation is .
Calculate .
Thus, .
Step 2: Evaluate .
In this expression, is raised to the power 4 first. Because 4 is an even number, results in a positive value, specifically:
.
Therefore, .
Step 3: Compare the results.
We now compare the two outcomes:
Both expressions evaluate to , hence they are equal.
Conclusion: and are equal. Therefore, the relationship is .
\( (-2)^7= \)
In -2⁴, the negative sign is outside the exponent, so you calculate 2⁴ = 16 first, then apply the negative: -16. In (-2)⁴, the entire -2 is raised to the 4th power, giving +16 since even powers of negatives are positive.
When you raise a negative number to an even power, the result is always positive! because negative times negative equals positive.
Think PEMDAS! Parentheses first, then Exponents, then Multiplication (including the negative sign). So -2⁴ means: do the exponent first (2⁴ = 16), then multiply by -1 to get -16.
Break it down step by step: First calculate , then apply the negative sign outside: . The outer negative flips the sign of whatever's inside.
Use parentheses to be crystal clear! Write -2⁴ as -(2⁴) and (-2)⁴ as (-2)⁴. This visual separation helps you see exactly what the negative sign applies to.
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