Answer :
Sure! Let's simplify each expression step-by-step and match them to the correct answer:
a. [tex]\( X^0 \)[/tex]
- Any non-zero number raised to the power of 0 equals 1.
- Simplified result: 1
- Matches with option 3: 1
b. [tex]\( (12x^3)^2 \)[/tex]
- First, raise each part inside the parentheses to the power of 2.
- [tex]\( 12^2 = 144 \)[/tex] and [tex]\( (x^3)^2 = x^{3 \times 2} = x^6 \)[/tex]
- Simplified result: [tex]\( 144x^6 \)[/tex]
- Matches with option 5: [tex]\( 144x^6 \)[/tex]
c. [tex]\( 2x^{-2} \)[/tex]
- A negative exponent means you take the reciprocal.
- [tex]\( x^{-2} = \frac{1}{x^2} \)[/tex]
- Simplified result: [tex]\( \frac{2}{x^2} \)[/tex]
- Matches with option 2: [tex]\( \frac{2}{x^2} \)[/tex]
d. [tex]\( 12x^2 \cdot (-5x^3) \)[/tex]
- Multiply the coefficients: [tex]\( 12 \times -5 = -60 \)[/tex]
- Add the exponents of like bases: [tex]\( x^2 \cdot x^3 = x^{2+3} = x^5 \)[/tex]
- Simplified result: [tex]\( -60x^5 \)[/tex]
- Matches with option 4: [tex]\( -60x^5 \)[/tex]
e. [tex]\( \frac{8x^{10}}{2x^2} \)[/tex]
- Divide the coefficients: [tex]\( \frac{8}{2} = 4 \)[/tex]
- Subtract the exponents of like bases: [tex]\( x^{10-2} = x^8 \)[/tex]
- Simplified result: [tex]\( 4x^8 \)[/tex]
- Matches with option 1: [tex]\( 4x^8 \)[/tex]
So each expression matches as follows:
- a. [tex]\( X^0 \)[/tex] = Matches with option 3
- b. [tex]\( (12x^3)^2 \)[/tex] = Matches with option 5
- c. [tex]\( 2x^{-2} \)[/tex] = Matches with option 2
- d. [tex]\( 12x^2 \cdot (-5x^3) \)[/tex] = Matches with option 4
- e. [tex]\( \frac{8x^{10}}{2x^2} \)[/tex] = Matches with option 1
a. [tex]\( X^0 \)[/tex]
- Any non-zero number raised to the power of 0 equals 1.
- Simplified result: 1
- Matches with option 3: 1
b. [tex]\( (12x^3)^2 \)[/tex]
- First, raise each part inside the parentheses to the power of 2.
- [tex]\( 12^2 = 144 \)[/tex] and [tex]\( (x^3)^2 = x^{3 \times 2} = x^6 \)[/tex]
- Simplified result: [tex]\( 144x^6 \)[/tex]
- Matches with option 5: [tex]\( 144x^6 \)[/tex]
c. [tex]\( 2x^{-2} \)[/tex]
- A negative exponent means you take the reciprocal.
- [tex]\( x^{-2} = \frac{1}{x^2} \)[/tex]
- Simplified result: [tex]\( \frac{2}{x^2} \)[/tex]
- Matches with option 2: [tex]\( \frac{2}{x^2} \)[/tex]
d. [tex]\( 12x^2 \cdot (-5x^3) \)[/tex]
- Multiply the coefficients: [tex]\( 12 \times -5 = -60 \)[/tex]
- Add the exponents of like bases: [tex]\( x^2 \cdot x^3 = x^{2+3} = x^5 \)[/tex]
- Simplified result: [tex]\( -60x^5 \)[/tex]
- Matches with option 4: [tex]\( -60x^5 \)[/tex]
e. [tex]\( \frac{8x^{10}}{2x^2} \)[/tex]
- Divide the coefficients: [tex]\( \frac{8}{2} = 4 \)[/tex]
- Subtract the exponents of like bases: [tex]\( x^{10-2} = x^8 \)[/tex]
- Simplified result: [tex]\( 4x^8 \)[/tex]
- Matches with option 1: [tex]\( 4x^8 \)[/tex]
So each expression matches as follows:
- a. [tex]\( X^0 \)[/tex] = Matches with option 3
- b. [tex]\( (12x^3)^2 \)[/tex] = Matches with option 5
- c. [tex]\( 2x^{-2} \)[/tex] = Matches with option 2
- d. [tex]\( 12x^2 \cdot (-5x^3) \)[/tex] = Matches with option 4
- e. [tex]\( \frac{8x^{10}}{2x^2} \)[/tex] = Matches with option 1
