Simplify using Exponent Rules. Write answer in Exponential Form. Help Video
(133)4
(133)4 can be simplified using the exponent rule for multiplication of powers.
The rule states that when you have a number raised to a power, and you raise that entire expression to another power, you can multiply the exponents.
In this case, we have (133) raised to the 4th power. So we can multiply the exponent 4 with the exponent of 133.
(133)4 = 133 * 4
Now, we calculate the value.
133 * 4 = 532
Therefore, the simplified exponential form of (133)4 is 532.
Simplify each expression using Exponent Rules. Choose the correct answer in the table.
(1 point)
512
57
5
53×54
5 to the 12th power – 5 cubed times 5 to the 4th power
5 to the 7th power – 5 cubed times 5 to the 4th power
5 – 5 cubed times 5 to the 4th power
(53)4
5 to the 12th power – open paren 5 cubed close paren to the 4th power
5 to the 7th power – open paren 5 cubed close paren to the 4th power
5 – open paren 5 cubed close paren to the 4th power
5453
5 to the 12th power – the fraction with numerator 5 to the 4th power and denominator 5 cubed
5 to the 7th power – the fraction with numerator 5 to the 4th power and denominator 5 cubed
5 – the fraction with numerator 5 to the 4th power and denominator 5 cubed
To simplify the given expression using exponent rules, let's break it down step by step:
5 to the 12th power – (5 cubed) times (5 to the 4th power)
First, let's simplify the parentheses by calculating 5 cubed (5^3) and 5 to the 4th power (5^4).
5 cubed = 5^3 = 5 * 5 * 5 = 125
5 to the 4th power = 5^4 = 5 * 5 * 5 * 5 = 625
Now, substitute the values back into the expression:
5 to the 12th power – 125 times 625
Next, perform the multiplication:
125 times 625 = 78125
Now, substitute the result back into the expression:
5 to the 12th power – 78125
Finally, calculate 5 to the 12th power by multiplying 5 twelve times:
5 to the 12th power = 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 = 244140625
Now, substitute the result back into the expression:
244140625 - 78125
To subtract these numbers, we need to ensure that we have the same base (5 in this case). To do this, we can rewrite 78125 as 78125 * 1, and rewrite 244140625 as 244140625 * 1.
244140625 - 78125 * 1
Now, we can subtract:
244140625 - 78125 = 244062500
Therefore, the simplified expression is 244062500, and the correct option in the table is:
- 5453 (fifth option in the table)
Choose the correct answer for each. Help Video(1 point)
1 -1 undefined
a0
1 – A to the 0 power
-1 – A to the 0 power
undefined – A to the 0 power
−(a)0
1 – negative A to the 0 power
-1 – negative A to the 0 power
undefined – negative A to the 0 power
00
1 – 0 to the 0 power
-1 – 0 to the 0 power
undefined – 0 to the 0 power
(−8)0
1 – negative 8 to the 0 power
-1 – negative 8 to the 0 power
undefined – negative 8 to the 0 power
−(−8)0
1 – negative negative 8 to the 0 power
-1 – negative negative 8 to the 0 power
undefined – negative negative 8 to the 0 power
Let's go through each option and determine the correct answer:
1. a^0: According to the exponent rule, any number raised to the power of 0 is equal to 1.
Therefore, the correct answer is: 1.
2. (-a)^0: According to the exponent rule, any number raised to the power of 0 is equal to 1.
Therefore, the correct answer is: 1.
3. 0^0: This is an indeterminate form. Different interpretations may yield different results.
Therefore, the correct answer is: undefined.
4. (-8)^0: According to the exponent rule, any number raised to the power of 0 is equal to 1.
Therefore, the correct answer is: 1.
5. (-(-8))^0: According to the exponent rule, any number raised to the power of 0 is equal to 1.
Therefore, the correct answer is: 1.
In summary, the correct answers are:
1. 1
2. 1
3. undefined
4. 1
5. 1
What is the missing exponent in the expression? Help Video
(x?)5=x20
(1 point)
To find the missing exponent, we can use the exponent rule for multiplication of powers. The rule states that when you have a variable raised to a power, and you raise that entire expression to another power, you can multiply the exponents.
In this case, we have (x?) raised to the 5th power, equal to x^20.
To find the missing exponent, we can set up an equation:
(x?)^5 = x^20
Now, we can use the exponent rule and equate the exponents:
? * 5 = 20
To solve for the missing exponent "?", we divide both sides of the equation by 5:
? = 20 / 5
Simplifying the right side of the equation gives:
? = 4
Therefore, the missing exponent in the expression (x?)^5 = x^20 is 4.