Which of the following is an equivalent expression to 7(−5.3)0+4⋅9 when applying the Zero Power Rule? (1 point)
Responses
70+4⋅9
Start Fraction 7 over 0 End Fraction plus 4 times 9
75.3+4⋅9
Start Fraction 7 over 5.3 End Fraction plus 4 times 9
71+4⋅9
Start Fraction 7 over 1 End Fraction plus 4 times 9
75.30+36
To apply the Zero Power Rule, any number raised to the power of zero is equal to 1.
In the expression 7(-5.3)0 + 4*9, the term (-5.3)0 can be simplified to 1.
So, the equivalent expression would be:
7 * 1 + 4 * 9
Simplifying further,
7 + 36 = 43
Therefore, the correct equivalent expression is 71 + 4*9.
Which of the following is an equivalent expression to 12(9−70)+(−29)0? (1 point)
Responses
12(9−1)−1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1
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
To simplify the expression 12(9-70) + (-29)0, we first need to perform the operations inside the parentheses.
9 - 70 = -61
Next, we can simplify (-29)0 using the Zero Power Rule. Any number raised to the power of zero is equal to 1.
(-29)0 = 1
Now we can substitute the simplified values back into the expression:
12*(-61) + 1
Multiplying -61 by 12 gives us -732:
-732 + 1
Finally, adding -732 and 1 gives us -731.
Therefore, the correct equivalent expression is 12(9-1)+1.
Which of the following shows the correct process of solving −4(3+120)+150 by generating an equivalent expression using the Zero Power Rule? (1 point)
Responses
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−16+1=−15
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 16 plus 1 equals negative 15
−4(3+120)+150=−4(15)+1=−60+1=−59
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 1 equals negative 60 plus 1 equals negative 59
−4(3+120)+150 =−4(15)+15=−60+15=−45
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 15 equals negative 60 plus 15 equals negative 45
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−4⋅5=−20
To solve the expression -4(3+120)+150 using the Zero Power Rule, we need to simplify the expressions inside the parentheses first.
3 + 120 = 123
Next, we can simplify (-4)(123) using the distributive property:
-4(123) = -492
Now we can substitute the simplified values back into the expression:
-492 + 150
Finally, adding -492 and 150 gives us -342.
Therefore, the correct equivalent expression is -4(3+120)+150=-492+150=-342.
Which of the following shows the correct process of solving −4(3+120)+150 by generating an equivalent expression using the Zero Power Rule? (1 point)
Responses
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−16+1=−15
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 16 plus 1 equals negative 15
−4(3+120)+150=−4(15)+1=−60+1=−59
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 1 equals negative 60 plus 1 equals negative 59
−4(3+120)+150 =−4(15)+15=−60+15=−45
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 15 equals negative 60 plus 15 equals negative 45
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−4⋅5=−20
To solve the expression -4(3+120)+150 using the Zero Power Rule, we need to simplify the expressions inside the parentheses first.
3 + 120 = 123
Next, we can simplify (-4)(123) using the distributive property:
-4(123) = -492
Now we can substitute the simplified values back into the expression:
-492 + 150
Finally, adding -492 and 150 gives us -342.
Therefore, the correct equivalent expression is -4(3+120)+150=-492+150=-342.
Which of the following shows the correct process of solving −4(3+120)+150 by generating an equivalent expression using the Zero Power Rule? (1 point)
Responses
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−16+1=−15
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 16 plus 1 equals negative 15
−4(3+120)+150=−4(15)+1=−60+1=−59
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 1 equals negative 60 plus 1 equals negative 59
−4(3+120)+150 =−4(15)+15=−60+15=−45
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 15 equals negative 60 plus 15 equals negative 45
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−4⋅5=−20
A B C or D?
The correct process of solving −4(3+120)+150 using the Zero Power Rule is:
−4(3+120)+150=−4(123)+150=−492+150=−342.
The correct response is not listed among the provided options.
To find an equivalent expression using the Zero Power Rule, we need to understand what the Zero Power Rule is. The Zero Power Rule states that any number (except zero) raised to the power of zero is equal to 1.
In the given expression, 7(−5.3)0 + 4⋅9, we can see that there is a term raised to the power of zero, which is (−5.3)0. Applying the Zero Power Rule, this term becomes 1.
Therefore, the equivalent expression would be:
7(−5.3)0 + 4⋅9 = 7(−5.3) + 4⋅9
Using this, we can simplify the expression to find the final answer.