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Which of the following is an equivalent expression to 7(−5.3)0+4⋅9 when applying the Zero Power Rule? (1 point)

Responses

75.30+36
Start Fraction 7 over 5.3 superscript 0 baseline End Fraction plus 36

70+4⋅9
Start Fraction 7 over 0 End Fraction plus 4 times 9

71+4⋅9
Start Fraction 7 over 1 End Fraction plus 4 times 9

75.3+4⋅9

3 answers

To analyze the expression \( 7(-5.3)^0 + 4 \cdot 9 \) and apply the Zero Power Rule, we know that any non-zero number raised to the power of 0 equals 1. Therefore, \( (-5.3)^0 = 1 \).

Substituting this back into the expression, we have:

\[ 7 \cdot (-5.3)^0 + 4 \cdot 9 = 7 \cdot 1 + 4 \cdot 9 = 7 + 36 = 43 \]

Now, let’s evaluate the provided options based on our simplification:

  1. 75.30 + 36: This simplifies to \( 75.3 + 36 \), which does not equal our result of 43.
  2. Start Fraction 7 over 5.3 superscript 0 baseline End Fraction plus 36: This suggests \( \frac{7}{(-5.3)^0} + 36 \), which translates to \( 7 + 36 \), not equal to 43.
  3. 70 + 4⋅9: This is equal to \( 70 + 36 \) which equals 106.
  4. Start Fraction 7 over 0 End Fraction plus 4 times 9: This is undefined as division by zero is not valid.
  5. Start Fraction 7 over 1 End Fraction plus 4 times 9: This suggests \( 7 + 36 \), which is equal to 43.
  6. 75.3 + 4⋅9: This simplifies to \( 75.3 + 36 \), which does not equal our result of 43.

The equivalent expression to \( 7(-5.3)^0 + 4 \cdot 9 \) when applying the Zero Power Rule is:

Start Fraction 7 over 1 End Fraction plus 4 times 9 (which equals \( 7 + 36 \)).

Which of the following is an equivalent expression to 12(9−70)+(−29)0? (1 point)
Responses

12(9−0)+0
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0

12(2)+1
Start Fraction 1 over 2 End Fraction left parenthesis 2 right parenthesis plus 1

12(9−1)+1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis plus 1

12(9−1)−1

To find an equivalent expression for \( 12(9 - 70) + (-29)^0 \), we first simplify the expression step by step.

  1. Evaluate the Zero Power: \((-29)^0 = 1\) (since any non-zero number raised to the power of zero is 1).

  2. Substituting the Zero Power Result: Now we can rewrite the expression: \[ 12(9 - 70) + 1 \].

  3. Simplify Inside the Parentheses: Calculate \( 9 - 70 \): \[ 9 - 70 = -61 \].

  4. Substituting Back: Now the expression is: \[ 12(-61) + 1 \].

  5. Calculate: While we won't strictly calculate this to a final number since we are looking for equivalent expressions, we note that the whole expression simplifies to: \[ -732 + 1 = -731 \].

Now, let's evaluate the provided options to determine which one is equivalent:

  1. \( 12(9 - 0) + 0 \): Simplifies to \( 12 \cdot 9 + 0 = 108 \), which is not equal to our result.

  2. Start Fraction 1 over 2 End Fraction left parenthesis 9 - 0 right parenthesis plus 0: Simplifies to \( \frac{1}{2}(9) + 0 = 4.5 \), which is not equal to our result.

  3. \( 12(2) + 1 \): Simplifies to \( 24 + 1 = 25 \), which is not equal to our result.

  4. \( 12(9 - 1) - 1 \): Simplifies to \( 12(8) - 1 = 96 - 1 = 95 \), which is not equal to our result.

None of the provided options represent an equivalent expression to \( 12(9 - 70) + (-29)^0 \).

However, if we were to find an error in the options (assuming +1 should be + 0 somewhere), the closest comparable treatment for format could be visible. But based on the inputs given, there appears to be no correct equivalent.

If these are the only options and I am to select one based on similar formatting or structure, please clarify if the starting expression includes additional conditions or if approximations yield something.