Q: How many tablespoons are equivalent to 3 ounces?

The correct answer is:6 tablespoons Explanation A US fluid ounce is a measure of volume: $1\ \text{fl oz} = 2\ \text{tbsp}$. So multiply that conversion by 3. Steps: Use the conversion: $$1\ \text{fl oz} = 2\ \text{tbsp}$$ Multiply by 3: $$3\ \text{fl oz} = 3 \times 2\ \text{tbsp} = 6\ \text{tbsp}$$ Therefore, 3 ounces equals 6 tablespoons.

Q: How many pounds is 62 kg?

The correct answer is: $136.6866025546241\text{ lb}$ Explanation We use the conversion factor $1\text{ kg} = 2.2046226218487757\text{ lb}$. Steps: Multiply the mass by the conversion factor: $$62\text{ kg}\times 2.2046226218487757\frac{\text{lb}}{\text{kg}} = 136.6866025546241\text{ lb}$$ Round as desired: to two decimal places $$\approx 136.69\text{ lb}$$ (to one decimal place $$\approx 136.7\text{ lb}$$). Therefore, 62 kg ≈ 136.69 lb (exactly about 136.6866 lb).

Q: Convert 165 pounds into kilograms.

The correct answer is: $74.84274105\text{ kg}$ Explanation We convert pounds to kilograms using the exact conversion factor $1\text{ lb} = 0.45359237\text{ kg}$. Multiplying 165 pounds by that factor gives the mass in kilograms. Steps: Use the conversion factor: $1\text{ lb} = 0.45359237\text{ kg}$. Multiply: $$165\times 0.45359237 = 74.84274105$$ Attach the unit: $74.84274105\text{ kg}$. Therefore, 165 pounds equals $74.84274105\text{ kg}$ (commonly rounded to $74.84\text{ kg}$).

Q: What is 300 milliliters in fluid ounces?

The correct answer is: $10.14\text{ US fl oz (approx.)}$ Explanation We convert using the US fluid ounce definition: $1\text{ US fl oz} = 29.5735295625\text{ mL}$, so multiply mL by the factor $1/29.5735295625 \approx 0.0338140226$. Steps: Multiply: $$300\text{ mL}\times 0.0338140226\frac{\text{US fl oz}}{\text{mL}}=10.14420678\text{ US fl oz}$$ Round to a sensible precision: $$\approx10.14\text{ US fl oz}$$ If you meant imperial (UK) fluid ounces instead: $$300\text{ mL}\div28.4130625\frac{\text{mL}}{\text{imp fl oz}}\approx10.56\text{ imp fl oz}$$

Q: What is 103 kg in lbs?

The correct answer is: $227.08\text{ lb}$ Explanation To convert kilograms to pounds multiply by the conversion factor $2.2046226218\text{ lb/kg}$. For 103 kg, multiply 103 by that factor and round to a convenient number of decimal places. Steps: Conversion factor: $1\text{ kg} = 2.2046226218\text{ lb}$ Multiply: $103\text{ kg}\times 2.2046226218\text{ lb/kg} = 227.0761300454\text{ lb}$ Round: $227.0761300454\text{ lb}\approx 227.08\text{ lb}$ Therefore, $103\text{ kg}\approx 227.08\text{ lb}$.

Question

Zero Exponent Rule | Overview & Examples

Accepted Answer

The zero exponent rule: For any nonzero number or expression $a$, $a^0 = 1$.

Explanation (intuitive + formal)

Intuitively: each time you decrease an exponent by 1 you divide by the base. For example:

$2^3=8$, $2^2=4$ (divide by 2), $2^1=2$ (divide by 2), and $2^0=1$ (divide by 2 again). The pattern forces $2^0$ to be 1.

Formal proof using laws of exponents:

For any $a\neq0$ and any integer $m$,

$$\frac{a^m}{a^m}=a^{m-m}=a^0.$$But $\frac{a^m}{a^m}=1$, so $a^0=1$.

Alternate proof using logarithms (for $a>0$):$$a^0=e^{0\ln a}=e^0=1.$$

Important exceptions and notes

The rule requires the base not be zero: $a^0=1$ only for $a\neq0$.
$0^0$ is indeterminate/undefined in most contexts (algebra, arithmetic). In combinatorics it is often assigned the value 1 by convention, and in limits calculus you must examine the limiting expression because different limits can give different values.
Negative bases work the same: $(-3)^0=1$.
Fractional or variable bases: $\left(\frac{1}{2}\right)^0=1$, $(5x)^0=1$ for any $x$ with $5x\neq0$.

Examples

$2^0=1$
$(-7)^0=1$
$\left(\frac{3}{4}\right)^0=1$
$(5x^2)^0=1$ provided $5x^2\neq0$ (i.e., $x\neq0$)
$0^5=0$ (note: exponent positive, base zero gives 0)
$0^0$ — undefined / indeterminate (context-dependent)

Related points

Negative exponents: $a^{-n}=\frac{1}{a^n}$. The zero exponent is the border case: $a^0=1$.
Any product or power that ultimately equals a nonzero base to the zero power equals 1: e.g., $(ab)^0=1$ if $ab\neq0$.

Quick practice (answers below)

Evaluate $3^0$.
Evaluate $( -2)^0$.
Simplify $\frac{5^3}{5^3}$.
Is $0^0$ equal to 1?

Answers:

$1$. 2. $1$. 3. $\frac{5^3}{5^3}=5^{3-3}=5^0=1$. 4. No — $0^0$ is indeterminate/undefined without extra context.

Tip: Whenever you see a nonzero expression raised to the zero power, replace it with 1. Always check the base before applying the rule (make sure it isn’t zero).